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Homework Help: Air resistance problem, expected time.

  1. Aug 1, 2009 #1
    1. The problem statement, all variables and given/known data
    As a bonus question on an assignment for my advanced physics class, we were asked to calculate (approx.) the expected time to impact of a drop of water falling 412m, from a tall building to the ground, considering linear drag. I've done most of the calculations but I expect that I'm missing something in the integrals. It's even more infuriating as they've given a "hint", and I still can't figure it out:

    integral, from 0 to t of (1-e-s/p)ds = t-p(e-t/p)

    which I worked out myself, so I can't quite figure out why they've given me this. Is it just that I can't rearrange this properly to give a value for t, or is there more to it?

    where p is the time constant, p= V/g = 3.374 = m/c where c = 1.55x10-7
    V= terminal velocity = 33.07ms-1
    g= gravitational acceleration= 9.8ms-2
    m= 5.23x10-7
    s= 412m= distance travelled (vertical)

    2. Relevant equations

    with the above, I also have the equations of motion obviously as well as:
    v = -V(1-e-t/p), where v is the velocity at any given point (intially 0)

    3. The attempt at a solution

    So far all I've worked out is the terminal velocity and time constant (given above)
    I think I need to use the height s (412m) and some relation between the time constant, terminal velocity and time but can't work through the maths.

    Thanks heaps
  2. jcsd
  3. Aug 1, 2009 #2


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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi emmaeng! Welcome to PF! :smile:

    I'm not sure why it's not working out for you, but it may be because this equation is wrong …
    if you put t = 0, you don't get 0, do you? :wink:
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